when taking \(Q_* \gg 1\)  in Eq. (REF ). By utilizing the same
techniques developed in Ref. [1]}, but now adapted to
the perturbation equations in DBIWI, we arrive similarly to the
result, when \(Q_* \gg 1\) , that \(\Delta _{\mathcal {R}}\)  is now given
by
\(\Delta _{\mathcal {R}} \simeq \Delta _{{\cal R},c=0}\left(\frac{Q_{*}}{Q_{c}}\right)^{3cc_{s*}^{2}},\) 
